Question

A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.

x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0



If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?

a
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.

b
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.

c
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.

d
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.

Answer 1

The end behavior of the polynomial function g(x) is that as x approaches negative infinity, g(x) approaches negative infinity, and as x approaches positive infinity, g(x) also approaches negative infinity.

Step-by-step explanation:

The end behavior of a polynomial function is determined by the leading term of the function. In this case, the given polynomial function has a positive leading coefficient, which means that as x approaches negative infinity, g(x) approaches negative infinity, and as x approaches positive infinity, g(x) also approaches negative infinity.